Post on 02-Feb-2021
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The Evolution of Power and the Divergence of
Cooperative Norms
Running Title: The Evolution of Power
Michael D. Makowsky1,*
and Paul E. Smaldino1,2,*
January 2015
1Center for Advanced Modeling in the Social, Behavioral, and Health Sciences,
Department of Emergency Medicine
Johns Hopkins University
5801 Smith Ave, Suite 3220, Davis Building
Baltimore, MD 21209 USA
2Department of Anthropology
University of California, Davis
1 Shields Avenue
Davis, CA 95616 USA
Corresponding author:
Michael D. Makowsky
Email: mmakowsky@jhu.edu
Phone: (410) 735-4012
* We thank Robert Axelrod, Robert Axtell, Brett Calcott, Joshua Epstein, Richard McElreath,
Peter Richerson, Matthew Zimmerman, workshop participants from the Institute for the Study of
Religion, Economics, and Society at Chapman University, and conference participants at
ASREC 2013 for comments. This project was supported by a Joshua Epstein’s NIH Director's
Pioneer Award (DP1OD003874). Java Code for the model is available from the authors upon
request.
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Abstract
We consider a model of multilevel selection and the evolution of institutions that distribute
power in the form of influence in a group’s collective interactions with other groups. In the
absence of direct group-level interactions, groups with the most cooperative members will
outcompete less cooperative groups, while within any group the least cooperative members will
be the most successful. Introducing group-level interactions, however, such as raiding or warfare,
changes the selective landscape for groups. Our model suggests that as the global population
becomes more integrated and the rate of intergroup conflict increases, selection increasingly
favors unequally distributed power structures, where individual influence is weighted by
acquired resources. The advantage to less democratic groups rests in their ability to facilitate
selection for cooperative strategies – involving cooperation both among themselves and with
outsiders – in order to produce the resources necessary to fuel their success in inter-group
conflicts, while simultaneously selecting for leaders (and corresponding collective behavior) who
are unburdened with those same prosocial norms. The coevolution of cooperative social norms
and institutions of power facilitates the emergence of a leadership class of the selfish and has
implications for theories of inequality, structures of governance, non-cooperative personality
traits, and hierarchy. Our findings suggest an amendment to the well-known doctrine of
multilevel selection that “Selfishness beats altruism within groups. Altruistic groups beat selfish
groups.” In an interconnected world, altruistic groups led by selfish individuals can beat them
both.
Keywords: multilevel selection; institutions; cultural evolution; conflict; agent-based modeling;
leadership
JEL Codes: C73, Z10
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1. Introduction
A hallmark of human societies is that individuals are structured into coherent groups,
often marked through language, dialect, or clothing (McElreath et al., 2003), and exhibit
preferential treatment of in-group members (Eaton, Eswaran et al. 2011). This group structure is
thought to play a large role in the extraordinary cooperation present among human societies (Hill
et al., 2011; Apicella et al., 2012; Moffett 2013), and has in turn contributed to our immense
success as a species (E. O. Wilson, 2012). Cooperation, however, goes hand in hand with
competition. Inter-group conflict in the form of raids, warfare, and conquest are among the most
important guiding forces in human cultural evolution (Tilly, 1975; Soltis et al., 1995; Turchin et
al., 2013). In a world where interactions between individuals are more often positive sum (e.g.,
production, trade), but the most salient interactions between groups are more likely to be
negative sum (e.g. warfare), the evolutionary forces selecting for individual and collective
strategies are likely to push in different directions.1 This raises two questions: 1) how does
intergroup conflict affect individual cooperative behavior, and 2) how do collective strategies
emerge from the preferences of a group’s individual members?
It is a well-documented result in the evolutionary sciences that groups that maintain
cooperative or altruistic norms of behavior have an evolutionary advantage over groups with
more selfish norms (Darwin 1871; Kropotkin 1905; Wilson & Wilson 2007). There has, in turn,
flourished a literature regarding the mechanisms by which a group can mitigate the free-riding
and parasitism that serve to undermine cooperation (Axelrod 1984; Henrich 2004; Nowak 2006;
Dugatkin 1997; Santos & Pacheco 2011; Smaldino et al. 2013; Smaldino & Lubell 2014;
1 This is not to say the individual interactions cannot be negative sum (e.g., theft) or that group interactions cannot
be positive sum (e.g., trade agreements). Nevertheless, between-individual cooperation and inter-group conflict are
widely considered to be among the most important factors, broadly speaking, in human social evolution (Choi and
Bowles 2007; Hill, Barton et al. 2009; Bowles and Gintis 2011; Turchin, Currie et al. 2013; Richerson, Baldini et al.
2014).
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Killingback et al. 2006; Aktipis 2004; Nowak & Sigmund 2005). This work has generally
regarded selfish strategies as something to be purged or marginalized to the periphery of the
group. In a world of both individual and collective interactions, however, a diversity of strategies
may yield evolutionary benefits. We propose an alternative model in which individual and
collective strategies can diverge, allowing cooperative norms to be maintained among the
majority while a persistent minority of selfish agents yields to the group a potential evolutionary
advantage. They do so via institutions that link wealth to power in collective decision making,
placing the group’s collective decisions in the hands of its most selfish members. In a world
where populations are increasingly interconnected, groups of individuals who can effectively
cooperate with outsiders in positive sum individual-level interactions, but are collectively
aggressive in negative sum group-level interactions can have a selective advantage over groups
that are either uniformly cooperative or uniformly aggressive at both the individual and group
levels.
Our research complements recent work indicating that cultural evolutionary models that link
individual-level behavior and group-level organization can shed light on the evolution of modern
social complexity (Choi & Bowles 2007; Bowles & Choi 2013; Turchin & Gavrilets 2009;
Turchin et al. 2013). We present a multilevel cultural evolutionary model that illuminates the
connection between prosociality, wealth, and institutions of power. The model is built on the
assumption that group-level institutions (North 1990; Bowles 2006; Smaldino 2014) facilitate
how strongly power in group-level decisions correlates to individual wealth, and that these
institutions fall along a continuum bounded by pure democracy and pure autocracy. Individuals
interact in positive sum cooperative games, groups interact in negative sum conflict games, and
collective strategies are directly connected to the strategies employed by group members. Our
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simulations suggest that, as the global population becomes more integrated and the rate of
conflict between groups increases, selection increasingly favors unequally distributed power
structures, with individual influence weighted by acquired resources. These structures allow
individuals to be more cooperative with outsiders through the emergence of a leadership class of
the selfish. Our findings offer an amendment to the doctrine of multilevel selection, summarized
by Wilson and Wilson (2007) as “Selfishness beats altruism within groups. Altruistic groups beat
selfish groups.” We would add: Altruistic groups led by selfish individuals can beat them both.
1.1. Institutions of Leadership and Power
Choi and Bowles (2007) demonstrate how warfare could have facilitated the evolution of
parochial altruism – i.e., the tendency to cooperate preferentially with members of the in-group
while promoting hostility toward individuals of other groups. In their model, inter-group
interactions resulted in war if a sufficient proportion of group members were parochial (i.e.,
hostile to outsiders). However, collective decisions, including the decision to go to war, are not
always decided by a majority vote. In this paper, we specifically focus on the group-level
institutions that translate individual proclivities for cooperation with outsiders into collective
decisions related to inter-group conflict.
Humans are unique in the possession of group-level institutions that designate leaders and
assign to them directive power over the group (Boehm & Flack 2010). Prior work on leadership
and human evolution has focused on within-group advantages to a hierarchical power structure.
Hooper et al. (2010) demonstrate that designation of a privileged individual to be responsible for
monitoring and punishment can stabilize cooperation in large groups in which peer monitoring
fails. In this case, we are not specifically looking at leaders as enforcers, but as individuals who
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make decisions on behalf of the group. A strong leadership may more efficiently consolidate
resources for more effective warfare (Tilly, 1975; Turchin, 2011), and it is likely that a broad
advantage of designating leaders to make collective decisions is to defray the transaction costs of
decision making (Coase 1937; Williamson 1975; Williamson 1981; Dow 1987; Van Vugt et al.,
2008).
This position raises the question: within whom should the group endow the power to
make decisions on their behalf? Should decisions be made democratically, representing the
average desires of the entire populace? Or should power in collective decisions be weighted
towards a select minority? We approach this question by investigating how institutions that link
power to individual resources may provide an evolutionary advantage to the group. Although
institutions are often discussed in terms of promoting cooperation (Axelrod and Keohane, 1985;
Bowles et al., 2003; Richerson & Henrich, 2012), institutions also can facilitate diversity in
social roles (North, 1990). The power structures that emerge from institutions are group-level
traits and are not reducible to properties of individuals (Smaldino, 2014). We make no
assumptions about how these institutions arise or how they are maintained. We note, however,
that once established, institutions may have a large degree of inertia because adopting new
institutions is a vast coordination problem.
A useful simplification is to classify institutions of power along a continuum representing
the degree to which power is concentrated among a subset of the group. A group whose
decisions represent the average inclinations of its members can be viewed as purely democratic.
On the opposite extreme, a group whose decisions reflect the sole inclination of a single
individual can be viewed as autocratic, with the understanding that this operational definition
ignores many of the organizational complexities associated with real autocratic regimes. A move
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from democratic to more autocratic institutions of power signifies a collective decision making
process that increasingly reflects the strategies of a shrinking fraction of the group.
1.2. Power and Cooperation in an Interconnected World
If today’s extant hunter-gatherer societies provide a good model for the ways in which
humans lived before the rise of agriculture, then it is reasonable to assume that early humans
lived according to highly democratic institutions of power. In his survey of modern-day foraging
tribes, Boehm (1999) found that institutions that promoted “reverse dominance hierarchies” – in
which individuals who tried to exert dominance over the group were punished – were ubiquitous.
With the rise of agriculture and increased warfare, human societies became much more
hierarchical, with privileged individuals deciding the fates of the communities that were
increasingly organized into chiefdoms and proto-states (Carneiro, 1970; Turchin & Gavrilets,
2009). Institutions of power became less democratic and more autocratic. Turchin and colleagues
(2013) have recently provided evidence for the theory that, after agriculture ended the need for
nomadism and facilitated the accumulation of wealth and the rise of technology, warfare
promoted the evolution of hierarchical organization of societies. Nevertheless, a puzzle remains
regarding the relationship between institutions of power and cooperation. In comparison to
larger-scale societies, small-scale societies are more insular, experiencing fewer interactions with
outsiders. Although there is evidence that contemporary foraging societies have frequent
ephemeral contact with outsiders (Fehr & Henrich, 2003), climate shifts in the Late Pleistocene –
the period immediately preceding the rise of agriculture – likely led societies to be relatively
isolated, both culturally and economically, in comparison to larger-scale societies (Boehm,
2012). In any case, it is uncontroversial to claim that larger-scale societies over the course of the
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last five millennia are characterized by substantially more contact with outsiders than are most
small-scale societies, and that this is true both in terms of inter-group interactions and
interpersonal interactions with extra-group individuals.
Small-scale societies are also more democratic than larger-scale hierarchical societies in
terms of how collective decisions are made (at least among men – there is often dramatic
inequity of power between males and females among foragers; Boehm, 1999).Yet these
democratic institutions of power are associated with less cooperation among individuals who are
not close kin, at least by the standards of economic games. A comparative study across 15
societies found that contributions in one-shot anonymous games of fairness (the Dictator,
Ultimatum, and Third-Party Punishment Games) were correlated with the degree to which
individuals tended to get their calories through market interactions as opposed to being home-
grown, hunted, or fished (Henrich et al., 2010). As the authors of that study note, “Although
frequent and efficient exchanges among strangers are now commonplace, studies of nonhuman
primates and small-scale societies suggest that during most of our evolutionary history,
transactions beyond the local group… were fraught with danger, mistrust, and exploitation” (p.
1480). In an isolated world, cooperation, particularly with outsiders, is risky business, and
democratic institutions of power are widespread. In contrast, in a more interconnected world
characterized by inter-group trade and war, and by less democratic institutions of power,
cooperation with both in-group individuals and outsiders is comparatively more common.
In this paper we present the foundations of a theory to explain this relationship between
cooperation, institutions of power, and the interconnected world. We theorize that increasing the
interconnectedness of global population through interpersonal trade and inter-group conflict
creates circumstances that give a selective advantage to undemocratic institutions of power,
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because they facilitate a power disparity that allows groups to be collectively aggressive in inter-
group conflicts while the majority of individuals can be highly cooperative, increasing the
overall resources available to the group. We support this theory with agent-based model
simulations.
2. The Model
We consider a simplified world of agents, each of whom belongs to a group and is
marked so as to be able to distinguish in-group members from outsiders. Model simulations run
in the absence of group markers are presented in the Supplementary Information. The world
initially contains M groups, each of which is initialized with n agents. Individuals pair up and
have individual-level interactions which represent opportunities for cooperation or exploitation,
and as modeled as a Prisoner’s Dilemma (PD) game. The relevant measure of interconnectedness
for individual-level interactions is the rate of population mixing, m, which is the degree to which
individuals are likely to have interactions with partners from outside their own group. After a
round of individual-level interactions there is the potential for group-level interactions. During
this, groups are randomly paired and engage in a Hawk-Dove (HD) game, which is a classic
model for inter-group cooperation, exploitation, and conflict. Here the relevant measure of
interconnectedness is the rate of conflict, γ, which is the probability that a round of group-level
interactions occurs for each round of individual-level interactions. Agents die if their resources
fall to zero or probabilistically with a rate that increases with age, and a group may go extinct if
all of its member agents die. Otherwise, payoffs from both individual- and group-level
interactions are accumulated by individuals and used for (asexual) reproduction, such that the
probability of reproducing increases with acquired resources. Offspring are born into the same
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group as their parents, and remain there throughout their lives. We also experimented with
migration as a robustness check, as it can be an important factor in evolutionary dynamics; we
will present these results later. Our model structure bears some resemblance to a framework
introduced by Simon and colleagues (2012). Their analyses indicate that due to the complexity of
its structure, an analytical approach to our model is not feasible, and that simulations are
required.
In addition to their group markers, each agent possesses two heritable traits, pin and pout,
representing the probability of cooperating in the individual-level PD game with an in-group or
out-group co-player, respectively. At the beginning of each simulation, each agent is initialized
with r0 resources and an age of zero. Each agent is also initialized with values for pin and pout,
each of which is a real number randomly and independently drawn from a uniform distribution in
[0, 1).
2.1. The distribution of power as cultural institution: powerGini
Each group is defined by a group-level institution relating individuals’ resources to power
in collective decision making during group-level interactions. These institutions are exogenously
imposed on each group and do not change. At the beginning of a round of group-level
interactions, all the n individuals in a group j are ranked according to their accumulated
resources, such that the agent i with the most resources has rankij = 1 and the agent h with the
least resources has rankhj = n. The distribution of power within a group stems from a fixed
cultural institution, implemented as the parameter power skew, σj, which translates an agent’s
ranking into the weight of its influence in collective decision making, so that the weight for an
agent i in group j is given by
𝑤𝑖𝑗 =(1+𝑛−𝑟𝑎𝑛𝑘𝑖𝑗)
𝜎𝑗
∑ 𝑘𝜎𝑗𝑛
𝑘=1
.
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While the power skew is a quantified metric determining how power is distributed within a
group, its scale does not have an immediately intuitive meaning in the context of real human
groups. For the sake of greater explanatory power, we adopt the Gini coefficient (Damgaard &
Weiner, 2000), a well-known statistic often used as a measure of inequality within a population,
to characterize and index a group’s distribution of power. We adopt this metric to represent the
disparity among individuals’ decision-making power within a group, and refer to this quantity as
the group’s powerGini. To compute this statistic for each group, we assumed that the initial
number of agents within a group, n, could be strictly ranked in terms of acquired resources
(although initially they all had equal resources, this would not be case for the majority for the
simulation run). We could then calculate each agent’s decision weight, wij, as described above.
The group’s powerGini is then given by:
𝐺 =∑ ∑ |𝑤𝑖𝑗 − 𝑤𝑘𝑗|
𝑛𝑘=1
𝑛𝑖=1
2𝑛2�̅�𝑗
where �̅� is the average decision weight in the group. A completely democratic group has
powerGini = 0, while groups grow increasingly autocratic as powerGini approaches 1 (the
algorithm used to ensure a nearly uniform distribution of group powerGini in the population is
given in the Supplementary Information). Throughout the rest of the paper, the distribution of
power in each group j is indexed as, and referenced by, its powerGinij.
2.2. Individual-level interactions
At the beginning of each time step, agents are paired using the algorithm described
below, and each pair then plays the PD game for resource payoffs.
2.2.1. Pairing algorithm. Let all the agents in a group j be represented by a vector Xj = [x1j, x2j,
…, xnj] where group j has n agents. For each group, the order of elements is randomized using a
pseudorandom number generator. A new vector, Y = [x1, x2, … xN], is then created by
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concatenating each vector Xj for all M groups in a random order. The vector Y therefore contains
all the live agents in the simulation, clustered by group. The elements in vector Y are then
shuffled such that each agent i, with probability m, swaps positions with a randomly selected
agent in Y. Finally, starting with the first agent in the newly shuffled Y, each agent with an odd-
number index is paired with the next (even-numbered) agent in the vector. When there are an
odd number of total agents, one agent will not play the PD game. Thus, when m = 0, almost all
pairings occur between agents of the same group, and when m = 1 pairings are completely
random.
2.2.2. Agent games. Each pair of agents play a standard prisoner’s dilemma (PD) game in which
the payoff for mutual cooperation is the reward R, the payoff for mutual defection is the
punishment P, and defecting against a cooperator results in the temptation T for the defector and
the sucker’s payoff S for the cooperator. A PD game is defined when T > R > P S and R > 2(T +
S), and is a positive-sum game. The probability that an agent cooperates is determined by
whether its co-player is a member of its group, as each agent i has two heritable traits
corresponding to the probabilities of cooperating with in-group (pin) and out-group (pout) co-
players. Each agent then chooses a move probabilistically and collects payoffs, which can
accumulate and be used for reproduction. Values for payoffs and other model parameters are
given in Table 1.
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Table 1. Model parameters.
Entity subfamily Description Symbol Value(s)
Global Initialization Number of groups M 50
Initial number of agents per group N 50
Agents’ initial resources r0 [14,24]*
Reproduction Maximum reproductive rate K 0.15
Standard deviation of mutation SDm 0.02
Reproduction growth rate B 0.2
Cost of reproduction cost_R [15,25] †
Amount of resources for maximal
reproductive rate ρ [30,50] ‡
Death Baseline probability of death δ 0.001
Max age maxAge 50
Agent games Population mixing rate m [0, 1]
PD Game payoff matrix T, S, R, P
T = 2, S = 0,
R = 1.5, P = 0.5
Group games Rate of conflict – the probability of a
round of between-group games for each
round of between-agent games γ [0, 1]
The returns to scale, based on total
resources, for intergroup conflict
(hawk-hawk) q 1
HD Game payoff matrix v, c v = 2, c = –3
Migration Probability of migration μ 0
Agent
Group ID
Accumulated resources ri
Age ai
Resources rank ranki
Probability of in-group cooperation pin
Probability of out-group cooperation pout
Group
Power skew σj
powerGini
* r0 = cost_R-1 † cost_R =15 + (10 ∙γ) ‡ ρ = 2∙cost_R, where † and ‡ reflect the calibration of simulation parameters to the rate of conflict so that the expected reproductive value from each step of the experimented was the
same across all experimental runs.
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2.3. Group-level interactions
A round of group-level interactions occurs with probability γ, the rate of conflict. In this
case, groups are paired randomly and play a HD game. If there is an odd number of extent
groups, one group will not be paired. Each group j’s move is determined by the composition of
its member agents and by its power skew, σj, which defines the agents’ weights of influence.
We explicitly connect collective behavior to individual strategies.2 We assume that
playing dove in an inter-group interaction is akin to cooperation in an individual-level
interaction, and that agents’ strategies for individual-level interactions with out-group co-players
are representative of their inclinations in group-level interactions. The probability that a group
plays dove is related to the out-group prosociality of its individual constituents, but in more
autocratic (less democratic) groups, individuals with more acquired resources have a greater
influence. Specifically, the probability that a group will play dove is given by:
𝑝𝑗 = ∑ 𝑝𝑜𝑢𝑡𝑖 ∙ 𝑤𝑖
𝑛
𝑖=1
We assume that groups interact because they are both interested in some resource, v. If
both groups are cooperative and play dove, they split the resource and each receive v/2. If one
group plays dove and the other aggresses and plays hawk, then the aggressive group takes the
2 Our theoretic model is built with individuals carrying a single strategy trait for out-group interactions, as
opposed to separate strategies for personal and collective interactions. This is because the selection
pressure on a collective behavior trait carried by an individual would have minimal fitness consequences
for the individual. As such it would be (within a cultural evolution model) effectively randomized relative
to individual behavior traits that are being selected for. This is likely our most controversial assumption.
We would also note that this assumption minimizes the cognitive costs, and cognitive dissonance, relative
to carrying two potentially opposing strategies, a non-trivial point given that boundedly rational agents
will often generalize strategies learned in one context to another less familiar context (Simon 1956;
Czerlinski, Gigerenzer et al. 1999; Bednar and Page 2007).
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entire resource and the cooperative group capitulates and gets nothing. If both groups play hawk,
then there is active conflict for the resources, which is costly for the loser. The winner of the
conflict receives the payoff v, but the loser receives a negative payoff –c, where c > v. Hence,
active conflict is risky, and is negative-sum. Each group’s members share equally in the costs
and benefits of large-scale inter-group conflicts (e.g., all agents receive v/2 resources when both
groups play dove). This is a simplifying assumption, as individuals may differentially share costs
and benefits through status or behavior (Mathew & Boyd, 2011). The winner of an active
conflict is determined probabilistically. We assume that larger groups with more resources will
tend to dominate smaller and poorer groups. The returns to scale are specified using methods
adopted from Hirschliefer (2000). In an active conflict between two groups (labeled 1 and 2
here), the probability that group 1 will win is given by:
Pr(1 𝑤𝑖𝑛𝑠) =𝑥1
𝑞
𝑥1𝑞 + 𝑥2
𝑞
where xj is the total resources of all the agents of group j (determined by summing the resources
of all the group’s agents), and q represents the returns to scale. For our simulations, we assumed
constant returns to scale, q = 1.
2.4. Death
An agent dies if its resources are less than or equal to zero. An agent may also die from disease
or happenstance, the chance of which increases with age. Mathematically, the chance of such a
death is given by:
Pr(𝑑𝑒𝑎𝑡ℎ)𝑖 = 𝛿𝑚𝑎𝑥𝐴𝑔𝑒−𝑎𝑖
𝑚𝑎𝑥𝐴𝑔𝑒
where δ is the baseline probability of death, ai is the number of time steps for which the agent
has been alive, and maxAge is the age at which the probability of death becomes one. For our
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simulations, we used maxAge = 50, with a average lifespan of 31.5 in the absence of resource-
related deaths. Note that our agents have neither developmental nor infertile periods, so this
lifespan represents active adulthood only.
2.5. Reproduction
An agent with sufficient resources (ri > cost_R) reproduces probabilistically, losing cost_R
resources in the process.3 A child agent is born into the same group as its parent, and begins with
r0 resources.4 An agent with sufficient resources reproduces with probability given by the logistic
function:
Pr(reproduce|𝑟𝑖) =𝐾
1 + 𝑒−𝐵(𝑟𝑖−𝜌)
where K is the maximum probability of reproduction, B is the rate of growth, and ρ is the amount
of resources corresponding to maximal growth in reproduction probability. In the experiments to
follow, ρ and cost_R are calibrated to the rate of conflict so that the expected reproductive value
from each step of the experimented was the same across all experimental runs.
An individual’s cooperative tendencies (pin and pout) are vertically transmitted (Boyd &
Richerson, 1985) from the agent’s parent with the potential for error (mutation). Mutation occurs
through the addition of an error term to both pin and pout. The error term is calculated
independently for each parameter and is drawn from a Gaussian distribution with mean of zero
and standard deviation SDm = 0.02. Both pin and pout were bounded in [0, 1].
2.6. Migration
3 In models of cultural evolution, resource-based (i.e., payoff-based) reproduction is equivalent to success-biased
imitation, in which the strategies of the most successful individuals are preferentially copied (Henrich and Gil-White
2001). 4 Another approach would be to initialize offspring with resources proportional to those of their parents. This
assumption is perhaps more realistic. However, because offspring inherit the strategies of their parents, proportional
resource allocation would create positive feedback in the evolutionary dynamics, giving much greater influence to
the wealthiest individuals in autocratic societies. While this description may indeed reflect reality in at least some
times and places, uniform allocation of resources to offspring provides a more rigorous test of our hypothesis, by
requiring individuals to pull themselves up by their bootstraps, their pockets unburdened by their pedigree.
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At each time step, μN agents are randomly selected, and each is reassigned to a randomly
selected group. A migrating agent forsakes its former group identity and joins the new group,
including associated group markers. Because destination groups are randomly selected from
among extant groups (those groups with a nonzero population), a “migrating” agent could
hypothetically remain in the same group. For most of the simulations presented, μ = 0.
3. Simulation Results
We ran 200 replicate simulations for each scenario reported, and the results presented are
averages from across those runs. Simulations were run for 300 time steps, which was sufficient
time for the distribution of agents across groups to reach a steady-state5 and for cultural, but not
genetic, evolution to occur (Perrault, 2012). The values of fixed parameters and the ranges of
tested parameters are summarized in Table 1.
3.1. Population-level results
We first consider the behavior of the average rates of in-group and out-group cooperation
(i.e., the average values for pin and pout) in the population in response to population mixing and
inter-group conflict. Averaging across all rates of conflict, we obtained the result that increased
population mixing selects for an increased in-group bias in individuals’ cooperative tendencies
(Fig. 1a). Competition between groups, in this case in the form of conflict, creates multilevel
5 The model reaches a steady state – a state of broken ergodicity (Axtell 2000), if you will – well before step 300,
typically between steps 150 and 200. While the relative distribution of population across groups reaches a steady
state, the overall population continuously grows. 300 time steps was chosen as the cutoff because it was safely after
a steady state was consistently reached, but before population growth reached a point of impractical computational
cost. We should also note that while the difference in rates of cooperation between groups reach a steady state, all
rates of cooperation across the entire population continue to decay, albeit at a slowing rate. This is largely a product
of the simplicity of the model – there is no agent learning, monitoring, or punishment in the model, and no
mechanism for purposely repeated interactions.
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selection pressures that reward groups who can collectively increase their total resources, which,
in the absence of considering institutions of power, is best accomplished through cooperation
with in-group members and defecting against out-group individuals (Hammond & Axelrod,
2006; Choi & Bowles, 2007).
Averaging across all rates of population mixing and focusing on the rate of conflict
indicates that increased inter-group conflict increases the rates of both in-group and out-group
cooperation, and has a larger effect on out-group cooperation, effectively decreasing the average
in-group bias in the population (Fig. 1b). This appears to contrast with other work indicating that
conflict should select for preferential cooperation with in-group individuals and increased
antagonism toward outsiders (Choi & Bowles, 2007; Gneezy & Fessler, 2012). However, this
prior work did not account for the presence of institutions of power. As the rate of conflict
increases, the premium on generating resources as a group becomes greater. It is therefore
important for group success that members maximize their productivity, even if doing so means
cooperating with outsiders from groups with whom their group may eventually be in conflict.
This is consistent with empirical results indicating the ascendance of cosmopolitan strategies
(i.e., cooperation with outsiders) in the presence of group-level conflict (Buchan et al., 2009; Pan
& Houser, 2013). As we will demonstrate, it is the presence of institutions of power makes this
rise of cosmopolitanism possible.
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Figure 1. Population structure influences cooperation. The average in-group and out-group cooperation
strategies as a function of (a) population mixing, averaged across rates of conflict, and (b) rate of conflict,
averaged across rates of population mixing.
3.2. Conflict influences institutional group differences
Here, we consider differential influence of increased rates of conflict on groups with
differently skewed institutions of power. Fig. 2 portrays three heatmaps, each corresponding to a
different group-level variable. For each graph, the x-axis refers to the powerGini of a given
group, varying between more democratic groups at the low end and more autocratic groups on
the high end. The y-axis refers to the rate of inter-group conflict. A useful interpretation is that
each row, corresponding to a given rate of conflict, is a portrait of a single condition of the
model, in which different group-level institutions can be compared.
As demonstrated above, in-group bias (defined as the average pin – pout) decreases with
the rate of conflict, as pout increases faster than pin. The upper right corner of Fig. 2a indicates
that under high conflict rates, groups with more autocratic power structures evolve less in-group-
biased cooperative strategies than do those with more democratic institutions. This is because
democratic groups cannot afford to be too cooperative toward outsiders in part because universal
cooperative norms would translate to playing dove too often in inter-group interactions and leave
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them open to exploitation (in addition to the risks of exploitation in individual-level interactions),
whereas more autocratic groups may be sheltered from the group-level effects of cosmopolitan
norms on their collective strategies. In more autocratic groups, the individuals who are the least
cooperative and therefore control the most resources (Nowak, 2006) will have more influence on
group-level decisions regarding conflict. Democratic groups, on the other hand, must be more
parochial, in part because being less cooperative toward out-group individuals leads to more
aggressive collective behavior in inter-group interactions. This connection between individual
and collective behavior is weakened in autocratic groups, allowing them to simultaneously
evolve more cosmopolitan interpersonal cooperation strategies (Fig. 2a) and more aggressive
collective strategies (Fig. 2b).
A more aggressive strategy means that a group will be less subject to exploitation by
other groups, but also creates an increased opportunity for active conflict, which can be quite
costly to the loser. More hawkish collective strategies will only benefit the group if it controls
enough resources so that it has a higher than average chance of winning active conflicts. When
the rate of conflict is high, there are more total resources available in the population, due to the
productive and technological benefits associated with inter-group trade and warfare. More
important to our argument is that when the rate of conflict is high, more autocratic groups control
more total resources compared with more democratic groups (Fig. 2c). This allows these groups
to benefit from being more hawkish.
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Figure 2. Rate of conflict differentially affects groups depending on power structure. Heatmaps
indicating the average (a) in-group bias among group members, (b) rate at which groups played Hawk in
inter-group interactions, and (c) the log10 total resources of the group, taken as a function of the rate of
conflict across all groups as identified by their powerGini. All data is averaged across rates of population
mixing.
3.3. An interconnected world selects for less democratic institutions of power
Fitness is, ultimately, measured by reproduction. When either population mixing or the
rate of conflict is low, a group’s institution of power has no significant influence (statistical or
otherwise) on its population. However, when both population mixing and the rate of conflict are
high, the log-transformed group population sizes are positively correlated with the group
powerGini (Figure 3).
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Figure 3. A relationship between reproductive success and undemocratic of power emerges only when
both population mixing and the rate of conflict are high. Scatterplots depict the log of groups’ populations
against their powerGini for low and high population mixing (0.1 and 1.0, respectively) and low and high
rates of conflict (0.1 and 1.0, respectively). This correlation was only statistically significant when both
mixing and conflict are high. Plot includes a bivariate linear model: logPopulation = β∙powerGini + ε. * denotes β significant at the p
23
selective advantage to less democratic groups, as individuals in those groups out-reproduced
those in more democratic groups, but neither condition is effective in the absence of the other.
Population mixing and intergroup conflicts are, as such, both necessary but not sufficient
conditions to yield an evolutionary advantage to less democratic institutions of power.
Figure 4. Population mixing and inter-group conflict select for undemocratic power structures.
Each cell of the heat map represents a different combination of the Rate of Conflict (x-axis) and
Population Mixing (y-axis) parameters. The color of the represents the mean population powerGini across
the 200 simulations using that parameter combination. Increased population mixing and rate of conflict
multiplicatively give a selective advantage to less democratic groups: individuals in those groups out-
reproduced those in more democratic groups.
3.4. Institutions of power and the divergence of cooperative norms
Our claim is that more autocratic institutions of power succeed in a more interconnected
world because they allow the less cooperative individuals to make group-level decisions
regarding conflict, allowing other individuals to be more cooperative. To examine this claim in
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more detail, we looked at the average levels of in- and out-group cooperation found among the
most and least cooperative members of each group. Figure 5 presents a series of scatterplots
depicting the average 1st through 99
th percentile distributions of the in- and out-group
cooperation strategies, as a function of group powerGini (population-level analyses showing
these percentile effects as a function of both the rate of conflict and the rate of population mixing
are presented in the Supplementary Information). The in-group and out-group strategies of the
least cooperative individuals in each group decline with powerGini (i.e., the 1st and 10
th
percentiles of cooperation are declining as groups become less democratic). At the same time,
the strategies of the most cooperative individuals in each group increase with powerGini (i.e.,
90th
, and 99th percentiles of cooperation are increasing as groups become less democratic).
These plots show a clear effect: Undemocratic institutions of power widen the distribution of
cooperative strategies, making the least cooperative individuals more selfish, and the most
cooperative individuals more cooperative.
3.5. Robustness to agent movement
In many species, group-level effects on selection are negligible, because high dispersal
and migration rates eliminate cohesive group structure. This is not the case for humans, however.
Indeed, there are numerous psychological and cultural mechanisms in place to maintain
affiliative identities among human groups (Durham 1991; Chudek & Henrich 2011), and these
identities act as powerful psychological motivators for social behavior (Tajfel et al. 1971; Brewer
2004). Nevertheless, humans do sometimes change their group identity through conversion or
migration, and this destabilization of group cohesion can act as a powerful force in cultural
evolution (Boyd & Richerson 2009; Hirschman 1970; Powell et al. 2009).
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In our baseline model, individuals interacted with members of other groups, but never
changed their group identity, reflecting the fact that cultural identities are strong and robust to
encounters with out-group members. It is important, however, to ensure that our results are
robust to a stronger type of migration, in which individuals can change group identities
(including group markers) so that their fates in inter-group interactions are tied to their adopted
rather than natal group. We ran simulations in which the probability of migration μ = 0.01. We
found that while migration added a small amount of noise, the results were qualitatively
unchanged.6
6 It is important to note that migration, in this context, is simply a form of noise added to the model to insure against
knife-edge results. A more meaningful model of migration would require purposeful movement and destination
decisions on the part of agents.
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Fig. 5. Undemocratic power structures widen the distribution of cooperation strategies, making the least
cooperative individuals more selfish and the most cooperative individuals more altruistic. Scatterplots
depicting the mean 1st through 99
th percentile of the distributions of (A) in-group and (B) out-group
cooperation strategies.
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4. Discussion
As the model’s population becomes more interconnected and the opportunities for
individual and collective interactions with outsiders increases, selection will increasingly favor
undemocratic institutions of power. As power in our model is concentrated within a shrinking
minority of a group’s wealthiest members, these institutions facilitate both an increase in the
variance of cooperative traits within the group and, in turn, a divergence of collective behavior
from average individual member behavior. These institutions yield groups in which the most
selfish, parochial members make collective decisions on behalf of a cooperative, cosmopolitan
populace. Our model demonstrates a mechanism through which a “leadership class of the
selfish” emerges, in effect insulating the majority of a group’s members and allowing the
evolution of more cooperative out-group strategies.
Our results impact broadly on the literature on the evolution of cooperation in humans.
This literature has been generally focused on the elucidation of mechanisms that can shift the
balance between cooperators and defectors to promote the evolution of cooperative strategies.
These mechanisms include reputation (Nowak & Sigmund, 2005; Smaldino & Lubell, 2014),
punishment (Boyd & Richerson 1992; Bowles & Gintis, 2004), unproductive costs (Aimone,
Iannaccone et al. 2013), and active avoidance of non-cooperators (Aktipis, 2004; Pepper, 2007).
These mechanisms are costly and as such minorities of non-cooperators typically remain,
however marginalized. The peripheral membership of non-cooperators, generally viewed as
parasitic, is, within the context of our model, a potential asset that is selected for at the group
level if their drag on interpersonal production is outweighed by their contribution towards
optimizing the group’s collective inter-group strategy. Consequently, we propose an addendum
to the widely accepted view concerning the evolution of cooperation and altruism in structured
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populations, summarized by Wilson and Wilson (2007) as “Selfishness beats altruism within
groups. Altruistic groups beat selfish groups.” We would add that in an interconnected world,
altruistic groups led by selfish individuals can beat them both.
In the absence of group-level interactions, groups with the most cooperative members
will outcompete less cooperative groups, while within any group its least cooperative members
will be its most successful7 (Nowak, 2006). The advantage to less democratic groups rests in
their ability to allow most of their members to cooperate – both among themselves and with
outsiders – in order to produce the resources necessary to fuel their collective success in inter-
group conflicts, while freeing their leaders from carrying those prosocial norms over to their
behavior in inter-group interactions. Less democratic groups are thereby able to leverage the
resources generated by their members’ cooperative interactions by granting greater influence to
those members who have accumulated the most resources – individuals who will inevitably be
those with the least cooperative strategy traits. This mechanism facilitates the separation of the
behavior of the collective from the behavioral norms of the majority of individuals populating
the group.
In an interconnected world, the most successful groups will collectively take on the
personality traits of their least cooperative members. Further to this point, we might begin to
think of sub-categories of non-cooperating individuals – and personality traits characterized as
Machiavellian, psychopathic, or narcissistic (the “dark triad”) – as minority traits selected for at
the group level (Paulhus & Williams, 2002), lending a new twist to adaptationist theories of
those traits (Wilson et al., 1996; Glenn et al., 2011; Gervais et al., 2013). Our model suggests
7 Within groups, selfish agents will outcompete cooperative agents only up to the point where their selfishness might
cause the entire group to go extinct, which contributes to the persistence of cooperative strategies in our model.
Moreover, the presence of iterated (selectively repeated) games would change the evolutionary dynamics, because
pairs of cooperators could outperform defectors. For simplicity, we have not explored this additional layer of model
complexity.
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that organizational frameworks that put more selfish individuals in charge of the group’s
collective decisions may be favored, as least in so far as those decisions are related to
cooperation and competition with other groups.
Although we predict that high interconnectedness will select for more plutocratic
institutions of power, the inverse is not explicitly supported by our model. In cases of low
interconnectedness, selection on group-level institutions of power is neutral, and therefore the
ubiquity of democratic and egalitarian institutions among foraging societies must be explained
through processes not fully captured by our model. Boehm (1999) has suggested that egalitarian
institutions foster norms of cooperation and trust within the group, and serve to minimize fitness
differences within the group while amplifying differences between groups, which facilitates
group-level selection for cooperation in the manner described by multilevel selection theory
(Wilson & Wilson, 2007). However, this cannot be the full story, as division of labor and the
consequent inequality can also have group-level benefits (Henrich & Boyd, 2008; Smaldino,
2014). It is likely that the stationary lifestyles and wealth accumulation associated with the
transition to agriculture at the dawn of the Holocene played some part in the transition from more
egalitarian to more skewed institutions of power (Richerson & Boyd, 1999; Bowles & Choi,
2013; Gowdy & Krall, in press).
4.1. Limitations and future directions
Our model explores the cultural evolution of institutions of power in response to broad
changes in between-group interactions. We do not provide a generative model for how these
latter changes came about, nor do we make any specific claims about the specific state of the
world either historically or presently. Indeed, our model applies just as readily to a world in
which intergroup conflict is decreasing. Nevertheless, the historical and archaeological record
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supports a world in which human groups experienced dramatic increases in their rates of
interaction with other ethnic and political groups (Johnson and Earle 2000; Horowitz 2001;
Bowles 2009). These changes occurred via complex, multistage processes involving
technological and infrastructural advances that are absent from our analysis. Because our model
merely assumes increased rates of inter-group interaction without specifying mechanism, our
results are entirely compatible with more specific mechanistic explanations for the evolution of
social complexity
Modeling social evolution necessitates presenting a highly simplified picture of the
world. We have not taken into account many important complexities, including norms of social
enforcement, contingent or adaptive strategies of cooperation, or the roles of technology or social
organization. Consideration of these factors underlies important questions that will form the
basis of future work.
For simplicity, we considered only two levels of organization and interaction: the
individual and group levels. While this is still one level more than most evolutionary population
models include, real human social organization is quite a bit more complicated. Both large- and
small-scale societies are hierarchically organized, with levels of organization ranging from
individuals and families through bands to multi-band societies in the case of hunter-gatherers
(Hamilton et al., 2007). These complexities in group structure will affect our characterization of
power and how it evolves – the full story will involve the transition from simple patterns of
asymmetry at the group level to power structures based on multiparty interactions and
assessments to the emergence of formalized leadership positions (Boehm & Flack 2010). We
also assume the existence of costless group markers. If group membership must instead be
established through the use of costly signaling and sacrifices, such as those fostered by religious
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rituals (Iannaccone 1992; Aimone, Iannaccone et al. 2013; Makowsky 2012; Sosis, 2003), then
the emergent social structures from those organizations may be opposed, both culturally and in
terms of cost tradeoffs, to institutions of power that would be optimal in the absence of costly
signaling.
Groups in our simulated world were initialized with a fixed institution of power. Details
related to how these institutions evolve endogenously within groups or spread between groups
were left out. Some models exist in which cooperative norms can spread through social learning
in a group-structured population (e.g., Boyd & Richerson, 2002), and similar models may be
useful for our purposes. A caveat, however, is that institutional evolution is complicated by the
fact that the adoption of a new institution is a group-level process that requires widespread
coordination. The details of warfare and resource allocation were also simplified for
convenience. In reality, smaller groups will have access to fewer resources, the risk of group-
level decisions may assessed before engaging in conflict, and allocation of the spoils of war or
conquest among the individuals within a groups may be heavily weighted to those with more
power. Future work will address details such as resource allocation, technology, and returns to
scale. Finally, our model only considers collective decisions related to inter-group conflict, and
does not address the many other group-level costs, benefits, and dynamics of various institutions
of power (see Acemoglu, 2008; Makowsky and Rubin 2013; Rubin 2014).
4.2. Concluding remarks
Autocracy, plutocracy, aristocracy, and other variants of top-heavy distributions of power
present a double-edged sword. Such skewed power distributions may facilitate an increasingly
interconnected world through positive feedback, by freeing the majority of citizenry to be more
cooperative in individual-level interactions, such as trade, with outsiders. While fostering
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cosmopolitan cooperation norms, however, these social institutions co-evolve with conflict and
aggression, imbuing the most selfish agents with the scale and power of their groups in contexts
within which they can be the most potentially destructive.
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Supplementary Information
S1. Algorithm for the initialization of group powerGinis.
In order to generate a distribution of powerGinis that were nearly uniformly distributed between
0 and 1, we used the following algorithm to generate each group’s power skew parameter.
s = smax /(M – 1); //increment
x = 0;
for j = 1:M //loop through